You can
put this solution on YOUR website!-\frac{1}{\sec(x)})
... Start with the given expression
}-\frac{1}{\frac{1}{\cos(x)}})
... Replace each secant with
}-\cos(x))
Multiply the second fraction by the reciprocal
}-\frac{\cos(x)\cdot\cos(x)}{\cos(x)})
... Multiply the second term by
}-\frac{\cos^2(x)}{\cos(x)})
Multiply
}{\cos(x)})
Subtract the fractions
}{\cos(x)})
Replace
)
with
)
So
-\frac{1}{\sec(x)}=\frac{\sin^2(x)}{\cos(x)})
Note: you can rewrite
as
\frac{\sin(x)}{\cos(x)})
and then rewrite as
\tan(x))
(using the identity
)
So this also means that
-\frac{1}{\sec(x)}=\sin(x)\tan(x))
(